In a wireless communication such as LTE, both the base station (also called the evolved Node B or eNodeB) and terminal (also called User Equipment or UE) are typically equipped with multiple antennas. This allows MIMO operation. The mobile terminals typically measure the downlink channels for each pair of antennas and derives a channel state report to send to the base station. The base station can then use this information for scheduling decisions such as:                Which terminals to transmit to;        Which frequency/time/code resources are used;        MIMO transmission mode (e.g. number of spatial streams, SU-MIMO or MU-MIMO).        
An effective method for capturing the channel state information is to select the entry from a codebook of precoders which, if applied at the transmitter, would lead to the highest data rate. The number of spatial streams assumed would typically be part of such a report.
Some codebook design issues for LTE-Advanced are considered in the following 3GPP documents:
[1]: R1−100083Precoding Codebooks for 8TX, (Marvell);[2]: R1−100051A Flexible Feedback Concept, (Ericsson,ST-Ericsson);[3]: R1−100022Codebook design for 8Tx DL MIMO, (CATT);[4]: R1−100251Extensions to Rel-8 type CQI/PMI/RI feedbackusing double codebook structure, (Huawei); and[5]: R1−100531DL Codebook Design for 8 Tx MIMO in LTE-A,(ZTE)
In LTE Release 8 a codebook is defined for the case of 4 antennas at the transmitter.
A modification of the method in [5] needs to be proposed to render the amended method more general and able to overcome the following problems:—                The new method has more design flexibility in selection of vectors (pairs of columns from a set of 4×4 matrices, rather than an 8×8 matrix) in order to optimise codebook design (e.g. for system performance)                    An additional parameter (specifying a phase rotation) can generate more vectors than are available using the method in [5]. The method of [5] effectively allows phase rotations of {1,−1}. We propose {1, j,−1,−j}.                        The new method does not need additional 2×2 matrices (e.g. five such are required in the example given in [5])        The new codebook coefficients can easily be constrained to an 8PSK alphabet (by limiting the constellation of the phase parameter)        The new design is more easily configurable to support different codebook sizes for different transmission ranks        